Answers
Explanation:
1) given:
y = (x + 3)^2 + (x + 4)^2
2) expand the binomials:
y = x^2 + 6x + 9 + x^2 + 8x + 16
3) add like terms:
y = 2x^2 + 14x + 25
4) take common factor 2 of the first two terms:
y = 2 (x^2 + 7x) + 25
5) complete squares for x^2 + 7x
x^2 + 7x = [x +(7/2)x ]^2 - 49/4
6) substitue x^2 + 7x = (x + 7/2)^2 - 49/4 in the equation for y:
y = 2 [ (x + 7/2)^2 - 49/4] + 25
7) take -49/4 out of the square brackets.
y = 2 (x + 7/2)^2 - 49/2 + 25
8) add like terms:
y = 2(x + 7/2)^2 + 1/2
And that is the vertex for of the given expression.
Related Questions
Alegbra 2 honors need help
Answers
(2^3)(2^-4) = 2^(3-4) = 2^-1 = 1/2
answer is D.
add exponents and keep the same base.then find the reciprocal and change the sign of the exponent
Answer:
Step-by-step explanation:
2^3)(2^-4) = 2^(3-4) = 2^-1 = 1/2
answer is D.
add exponents and keep the same base.then find the reciprocal and change the sign of the exponent
the public library has an approximate length of 1 x 10^5 millimeters and width of 8 x 10^4 millimeters. what is the area, in square milliters, of the public library?
a. 8 x 10^9 square millimeters
b. 9 x 10^9 square millimeters
c. 8 x 10^20 square millimeters
d. 9 x 10^20 square millimeters
Answers
.. = (1*10^5 mm)*(8*10^4 mm)
.. = (1*8)*10^(5+4) mm^2
.. = 8*10^9 mm^2
Selection A is appropriate.
Helen's Shop is 60 meters wide and 80 meters long. The parking lot in front of Helen's Shop is twice as long as it is wide and is 50 meters wide.What is the sum of the area of Helen's Shop and the parking lot?
Answers
Answer:
9,800
Step-by-step explanation:
Helen's Shop
60 m x 80 m = 4,800 m2
Parking Lot
Length = 2 × 50 m = 100 m
Area = 50 m × 100 m = 5,000 m2
Final Answer
4,800 m2 + 5,000 m2 = 9,800 m2
Suppose a life insurance company sells a $250,000 one-year term life insurance policy to a 20-year-old female for $320. The probability that the female survives the year is 0.999647. Compute and interpret the expected value of this policy to the insurance company.
Answers
do you agree? explain why or why not
Answers
square root of 2(4)+1 = square root of 9 = 3
3+3 = 6
and 6 is not 0 so x cannot = 4
A student concluded that the solution of the equation [tex]\sqrt{2x+1}+3 = 0[/tex] is x = 4. The conclusion is true.
What is a perfect square?Perfect squares are those integers whose square root is an integer.
Let x-a be the closest perfect square less than x,
and let x+b be the closest perfect square more than x, then we get x-a < x < x+b (no perfect square in between x-a and x+b, except possibly x itself).
Then, we get:
[tex]\sqrt{x-a} < \sqrt{x} < \sqrt{x+b}[/tex]
[tex]\sqrt{2x+1}+3 = 0\\\\\sqrt{2x+1}= -3[/tex]
by taking square on both sides we get
[tex](\sqrt{2x+1})^2 = (- 3)^2 \\\\2x+ 1 = 9[/tex]
when x = 4
2(4) + 1
= 9
Thus, the solution of the equation is 4.
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When disposal materials are dropped more than 20 feet to an exterior location, an enclosed chute must be used. true or false?
Answers
The assertion is not totally true.
It is not always necessary to dispose of debris dropped more than 20 feet to the outside using an enclosed chute.
It is crucial to check the precise restrictions that apply in your area as building codes and regulations might differ based on the jurisdiction.
It is important to keep in mind that, in some circumstances, a covered chute may be necessary for safety reasons or to stop the materials from spreading or causing harm while being disposed of.
These specifications may be unique to certain locales, building types, or construction projects.
Therefore, it is crucial to check your area's construction laws and regulations to ascertain the precise specifications for disposal requirements.
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What is 1 17/24 simplified
Answers
1(17/24) simplified is 41/24.
We have,
To simplify the mixed number 1 17/24, we need to convert it to an improper fraction.
To do that, we multiply the whole number (1) by the denominator of the fraction (24), and then add the numerator (17):
1 x 24 + 17 = 24 + 17 = 41
So, the mixed number 1 17/24 is equivalent to the improper fraction 41/24.
Therefore,
1(17/24) simplified is 41/24.
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Which rule describes the translation? T–3, –2(x, y) T–3, 2(x, y) T3, –2(x, y) T3, 2(x, y)
SOMEONE PLEASE ANSWER PLEASE
Answers
The rule which describes the translation of the figure is T–3, –2(x, y).
The translation T(x, y) → (x – h, y – k) moves a point (x, y) to a new point (x – h, y – k).
T–3, –2(x, y) moves the point 3 units to the right and 2 units down.
T–3, 2(x, y) moves the point 3 units to the right and 2 units up.
T3, –2(x, y) moves the point 3 units to the left and 2 units down.
T3, 2(x, y) moves the point 3 units to the left and 2 units up.
So the answer is T–3, –2(x, y).
Here is a table that shows the effect of each translation on the point (3, 4):
Original point | Translation | New point
(3, 4) | T–3, –2(x, y) | (0, 2)
(3, 4) | T–3, 2(x, y) | (6, 6)
(3, 4) | T3, –2(x, y) | (6, 2)
(3, 4) | T3, 2(x, y) | (0, 6)
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Solve the following equation : 7x/15-1=22
Answers
-----------------
To solve this all it takes is two simple steps
Simplify [tex] \frac{7x}{15-1} =22[/tex]
1/2x =22
------------------------
Multiply both sides by 2
2 · [tex] \frac{1}{2} [/tex] = 2 · 22
x = 44
[tex]\boxed{\boxed{Rearrange \ the \ equation \ by \ subtracting}}[/tex]
[tex] \left[\begin{array}{ccc}\boxed{\boxed{ 7*x/15-1-(22)=0 }}\end{array}\right] [/tex]
[tex]\boxed{((7* \frac{x}{15)}-1)-22=0}} [/tex]
[tex] \left[\begin{array}{ccc} \frac{(7x - 15) }{15} -22=0\end{array}\right] [/tex]
[tex]Add \ 345 \ to \ both \ sides \ of \ the \ equation : \\ \\ 7x = 345 \\ \\ Divide \ both \ sides \ of \ the \ equation \ by \ 7: x = 345/7 = \boxed{\boxed{49.28}} [/tex]
Hope this helps you!
Tina bought two sweaters for $15.50 each and a skirt for $19. What
was the total amount of her bill if she had to pay a sales tax of
5.75%?
a. $36.40
b. $50
c. $52.88
d. $56.40
HELP ASAP ANSWER IS NOT A
Answers
I need help with finding Angle B
Answers
notice that, the diagonal is really just a traverse line cutting through the parallel segments of AB and DC, and since those angles are alternate interior ones, that means 5y - 1 = 7y - 15, and 6x - 6 = 4x + 2, therefore
[tex]\bf 5y-1=7y-15\implies 14=2y\implies \cfrac{14}{2}=y\implies \boxed{7=y} \\\\\\ 6x-6=4x+2\implies 2x=8\implies x=\cfrac{8}{2}\implies \boxed{x=4}\\\\ -------------------------------\\\\ \measuredangle BAC = 5(7)-1\implies 34\qquad \measuredangle BCA=4(4)+2\implies 18 \\\\\\ therefore\qquad \measuredangle B=180-\measuredangle BAC-\measuredangle BCA[/tex]
given the conversion factor 3.28 ft/ 1m which cube above has the larger surface area
cube A is 7’ cube b is 2m
Answers
We have then:
Cube A:
7 * (1 / 3.28) = 2.13 m
Cube B:
2 m
The surface area of a cube is:
A = 6 * L ^ 2
Where,
L: side
Since cube A has a longer side (2.13m) then it will have the largest surface area.
Answer:
Cube A has the larger surface area
Final answer:
After converting Cube B's side length to feet, Cube A has a surface area of 294 ft² while Cube B has a surface area of 258.2016 ft², making Cube A the one with the larger surface area.
Explanation:
To determine which cube has the larger surface area, we must work with a common unit of measurement for both cubes. We'll convert Cube B from meters to feet using the conversion factor 3.28 ft/1m.
For Cube A with a side length of 7 feet, the surface area (SA) is calculated by the formula SA = 6 × s² (where 's' is the side length).
SA (Cube A) = 6 × (7 ft)² = 6 × 49 ft² = 294 ft².
For Cube B with a side length of 2 meters, we first convert meters to feet: 2 m × 3.28 ft/m = 6.56 ft. So, the surface area of Cube B becomes:
SA (Cube B) = 6 × (6.56 ft)² = 6 × 43.0336 ft² = 258.2016 ft².
Between Cube A and Cube B, Cube A has the larger surface area.
helpppppppppppppppppppppppppp
Answers
3x^2 (y^5)^1/4 which is the first choice
Explanation:
The fourth root means that the bracket under has the root has a power of 1/4.
So, the given expression is:
(81 * x^8 * y^5)^1/4
Now, we will distribute the power as follows:
(81 * x^8 * y^5)^1/4 = (81)^1/4 * (x^8)^1/4 * (y^5)^1/4
= 3 * x^2 * y^5/4
This expression is equivalent to:
3x^2 (y^5)^1/4 which is the first choice
Hope this helps :)
Quadrilateral ABCD is inscribed in this circle.
What is the measure of ∠A
Answers
106 degerees.
m<A + m<C = 180
m<A + 74 = 180
m<A = 106
22 gallons of gas cost $65.56 what is the unit rate for one gallon of gas
Answers
If we would want to find out what it would be, we would have to divide it.
Your correct answer would be (2.98)
I did 65.56/22.
Hope this helps you!
When you find the unit rate, you have the input factor, (or the unit you want to find) equal to 1.
22/22= 1
Divide the price of the gas $65.56 by 22.
65.56/22= 2.98
Each gallon of gas is $2.98.
I hope this helps!
~kaikers
What is the cricket’s hang time (amount of time the cricket is airborne)? Round to the nearest thousandth h(t) = –16t2 + 14t
Answers
h(t) = –16t² + 14t
using a graph tool
see the attached figure
the cricket’s hang time is the difference between point (0,0) and (0.875,0)
(0.875-0)=0.875 sec
the answer is 0.875 sec
The hang out time is 0.875 sec.
What is Quadratic equation?An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term. First, there must be a term other than zero in the coefficient of x²(a>0) for an equation to be a quadratic equation. The x² term is written first when constructing a quadratic equation in standard form, then the x term, and finally the constant term. The numerical values of a, b, and c are often expressed as integral values rather than fractions or decimals.
Given Equation:
h(t) = –16t² + 14t
For the Hangout time we can consider the function h(t)=0
0 = –16t² + 14t
16t² = 14t
16t= 14
t= 14/16
t= 0.875 sec
Hence, the hang out time is 0.875 sec.
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Classify the model as exponential growth or exponential decay. Identify the growth or decay factor AND the percent of increase per time period.
y=10(0.2)^t
Plz help!
Answers
The decay factor is 0.2.
The change per period is (0.2 -1)*100% = -80%. The negative sign means it is a decrease of 80% per period.
Don't want any answers, just how to solve, step by step. please :)
Answers
Help, what even is this?
Answers
If [tex]0 \ \textless \ t \le 30[/tex] then f(t) = 0. This means that for the first 30 minutes, the cost is $0, in other words the first half hour is free.
If [tex]30 \ \textless \ t \le 90[/tex] then f(t) = 5 indicating that the cost is $5 for the entire span from 30 minutes to 90 minutes (excluding t = 30 but including t = 90). Choice B is not the answer because the cost isn't $5 per minute. The cost for this entire timespan is simply $5
Finally, if t > 90, then f(t) = 10 telling us that any time value over 90 minutes will have the cost be $10. This is why the answer is choice D
Elio makes candles that are 14 cm tall. Each candle burns 8 hours before going out. He is wondering how many hours a 21 cm tall candle can burn for. He assumes that the relationship between the height of a candle and number of hours it burns (h) is proportional. How long can a 21 cm tall candle burn for?
Answers
Find the unit rate
14 ÷ 8 = 1.75 cm/h
Divide
21 ÷ 1.75 = 12
You can set this up as an algebraic equation to check the answer.
If the candle is 21 cm tall, it will burn for 12 hours.
Hope this helped you! :)
algebra 2 unit 2 question. connexus.
Answers
The correct answer is the first option: y=(2x-1)(2x-3)(2x+5)
Because: if you give values to the variable "x" and graphic each point calculated, you will obtain the graph above. For example:
If x=-3/2:
y=(2x-1)(2x-3)(2x+5)
y=(2(-3/2)-1)(2(-3/2)-3)(2(-3/2)+5)
y=48 (As you can see in the graph)
If x=0:
y=(2x-1)(2x-3)(2x+5)
y=(2(1)-1)(2(1)-3)(2(1)+5)
y=15 (It is shown in the graph)
If x=1:
y=(2x-1)(2x-3)(2x+5)
y=(2(1)-1)(2(1)-3)(2(1)+5)
y=-7 (As you can see the graph attached)
Which expression is equivalent to the expression below?
Answers
Answer:
C. [tex]\dfrac{1}{(m-4)(m-3)}[/tex]
Step-by-step explanation:
First note that
[tex]m^2-16=(m+4)(m-4) \quad \text {and} \quad m^2-9=(m+3)(m-3)[/tex]
On the other hand, the expression from the question is equivalent to
[tex]\dfrac{m+3}{m^2-16} \cdot \dfrac{m+4}{m^2-9}=\dfrac{m+3}{(m+4)(m-4)}\dfrac{m+4}{(m+3)(m-3)}[/tex]
we cancel the equal terms in the numerator and the denominator and finally we get that our expression is equivalent to
[tex]\dfrac{1}{(m-4)(m-3)}[/tex]
This figure shows circle O with diameter QS . mRSQ=290∘ What is the measure of ∠ROQ ? Enter your answer in the box. °
Answers
we know that
mRSQ=290°
and
mRSQ+mORQ=360°
therefore
mORQ=360°-mRSQ---------------> mORQ=360°-290°=70°
the answer is 70°
Answer: 70 I just took the test!
Step-by-step explanation:
The difference of the squares of two positive consecutive even integers is 76. find the integers. use the fact that, if x represents an even integer, then x+2 represents the next consecutive even integer.
Answers
(x + 2)² - x² = 76
We should find the value of x to know the smaller integer.
(x + 2)² - x² = 76
simplify the quadratic expression for (x + 2)²
(x + 2)² - x² = 76
(x + 2)(x + 2) - x² = 76
x² + 2x + 2x + 4 - x² = 76
x² - x² + 4x + 4 = 76
4x + 4 = 76
Solve for x
4x = 76 - 4
4x = 72
x = 72/4
x = 18
Find the bigger integer
x + 2 = 18 + 2 = 20
The integers are 18 and 20
The two positive consecutive even integers that, when their squares are subtracted, equal 76 are 18 and 20.
Explanation:In this problem, the two positive consecutive even integers can be represented as x and x+2. The problem states that the difference of their squares is 76, which can be put into the equation (x + 2)^2 - x^2 = 76. By simplifying this equation, we get 4x + 4 = 76. Solving for x, we find that x = 18. Therefore, the two consecutive even integers are 18 and 20.
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Most evenings after dinner Duarte spends 30 minutes playing chess with his dad.
Write an equation for the number of minutes, m, that Duarte spent playing chess with his dad if they played chess together e
evenings.
Answers
e= # evenings played
m= # minutes played
Total equals number of evenings played multiplied by number of minutes plated per evening.
EQUATION:
t=e * m
EQUATION (if 30 minutes per evening):
t=30e
Example:
3 nights, 30 minutes played
t= 3 * 30
t=90 minutes total played
Hope this helps! :)
Consider a function that describes how a particular car’s gas mileage depends on its speed. What would be an appropriate domain for this function?
Answers
o to 100 miles per hour
What single transformation is required to map one of these congruent triangles onto the other?
Answers
why?? because i is just like a mirror it is reflected on the other side
Answer:
its reflection
Step-by-step explanation:
I did it on edge ; )
is y=0.8(2.1)x exponential growth or exponential decay
Answers
______________________________________________________
Given: y = (0.8)(2.1)ˣ
______________________________________________________
Let us make a table and plug in some "x" values and see what the "y" values are:
______________________________________________________
x | y
_______________
1 | 1.68
_______________
2 | 3.528
_______________
3 | 7.4088
__________________________________________________________
The answer is: "exponential growth" .
__________________________________________________________
As "x" increases, "y" increases (by more than a linear relationship/proportion).
__________________________________________________________
A drawer contains 9 black socks, 8 gray socks, and 7 blue socks. Without looking, you draw out a sock and then draw out a second sock without returning the first sock. What is the probability that the two socks you draw are the same color?
Answers
First of all, there are total 9 + 8 + 7 = 24 socks.
Probability of a black socks in a row is 9/24
Probability of the second black socks without replacement, if first one was black, is 8/23
Therefore the probability of the 2 black socks in a row are 3/23 (I multiplied the two)
Using the same technique, the p of 2 gray socks are 7/69
The p of 2 blue socks are 7/92
Now you add them up, and you get 85/276 as your answer
Let me know if there are any other questions!
You and a friend tutor for a total of 12 hours. Use the tape diagram to find how many hours you tutor.
Answers
I teach 9 and 6 hours respectively
Left diagram:
In this diagram you show three quarters of the hours.
We have then:
(3/4) * (12) = 9
Answer:
You teach 9 hours.
Right diagram:
In this diagram you teach half of the hours.
We have then:
(2/4) * (12) = 6
Answer:
You teach 6 hours
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You tutored for 6 hours, your friend tutored for 6 hours as well.
Image:
You and a friend listen for a total of 2 hours.
You
Friend
You
The image shows a tape diagram with two sections labeled "You" and "Friend". The "You" section is longer than the "Friend" section, indicating that you tutored for more hours than your friend.
To find the number of hours that you tutored, we can divide the total number of hours tutored (12 hours) by the number of sections in the tape diagram (2).
Number of hours you tutored = 12 hours / 2 sections = 6 hours
Therefore, you tutored for 6 hours.
Explanation of tape diagrams:
A tape diagram is a visual representation of a mathematical equation. It is a horizontal bar that is divided into sections, with each section representing a different quantity. The length of each section represents the size of the quantity it represents.
Tape diagrams can be used to solve a variety of mathematical problems, including addition, subtraction, multiplication, and division problems. They are especially useful for solving problems that involve multiple quantities, as they can help to visualize the relationships between the different quantities.
In this case, the tape diagram is used to solve the following problem:
> You and a friend tutor for a total of 12 hours. Use the tape diagram to find how many hours you tutor.
The tape diagram is divided into two sections, one for you and one for your friend. The length of each section represents the number of hours that each person tutored. Since you tutored for more hours than your friend, the "You" section is longer than the "Friend" section.
To find the number of hours that you tutored, we can divide the total number of hours tutored (12 hours) by the number of sections in the tape diagram (2). This gives us the number of hours that you tutored, which is 6 hours.
Therefore, the answer to the question is "You tutored for 6 hours."
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